Lemarié's Wavelet

A wavelet used in multiresolution representation to analyze the information content of images. The Wavelet is defined by

$\begin{displaymath} H(\omega)=\left[{2(1-u)^4{315-420u+126u^2-4u^3\over 315-420v+126v^2-4v^3}}\right]^{1/2}, \end{displaymath}$

where

$\displaystyle u$	$\textstyle \equiv$	$\displaystyle \sin^2({\textstyle{1\over 2}}\omega)$
$\displaystyle v$	$\textstyle \equiv$	$\displaystyle \sin^2\omega$

(Mallat 1989).

See also Wavelet

References

Mallat, S. G. ``A Theory for Multiresolution Signal Decomposition: The Wavelet Representation.'' IEEE Trans. Pattern Analysis Machine Intel. 11, 674-693, 1989.

Mallat, S. G. ``Multiresolution Approximation and Wavelet Orthonormal Bases of $L^2(\Bbb{R})$ .'' Trans. Amer. Math. Soc. 315, 69-87, 1989.